Simplify the following expression: $p = \dfrac{x^2 - 8x - 9}{x - 9} $
Solution: First factor the polynomial in the numerator. $ x^2 - 8x - 9 = (x - 9)(x + 1) $ So we can rewrite the expression as: $p = \dfrac{(x - 9)(x + 1)}{x - 9} $ We can divide the numerator and denominator by $(x - 9)$ on condition that $x \neq 9$ Therefore $p = x + 1; x \neq 9$